Surveying of boreholes using shortened non-magnetic collars

ABSTRACT

.[.When surveying a borehole using an instrument responsive to the earth&#39;s magnetic field, a length of non-magnetic drill collar is necessary to house means for measuring the magnetic field in the borehole perpendicular to the direction of the borehole axis. The instrument determines the inclination angle and the highside angle from the gravitation measurements, with these measurements and the magnetic measurements, the azimuth angle is determined. Using the method of this invention a minimum length of non-magnetic material necessary for an accurate measurement may be calculated and used..]. .Iadd.Disclosed are method and apparatus for surveying a borehole including use of a survey instrument for making gravitational measurements from which the inclination and highside angles of the instrument may be determined. Measurements of two components of the local magnetic field perpendicular to the longitudinal axis of the instrument may be sensed with the instrument, and may be used to determine the azimuth angle of the instrument under the assumption that magnetic interference due to the pipe string in which the instrument is located lies solely along the longitudinal axis of the instrument. The accuracy of the azimuth determination may be enhanced by an iteration process. To the extent that the pipe string interference includes transverse field components at the instrument, the sensors of the instrument may be separated from such pipe string members by placing the instrument in non-magnetic material whose minimum length may be determined. .Iaddend.

.Iadd.This is a continuation of co-pending application Ser. No.06/892,502 filed on Aug. 1, 1986, now abandoned; which is a reissue ofSer. No. 06/516,716 filed 7/20/83, now U.S. Pat. No. 4,510,696..Iaddend.

This invention relates to the surveying of boreholes and to the use of ashorter nonmagnetic drill collar for housing the surveyinginstrumentation. It is particularly concerned with the determination ofthe azimuth angle of a borehole using a shorter nonmagnetic drillcollar.

At present "pivoted compass" single shot and multishot instruments areused for determination of azimuth angle. However, with such instruments,the necessary correction to compensate for the modification of theearth's magnetic field in the vicinity of the instruments can only beperformed by assuming the size and direction of the error field causedby the instrument, requiring a knowledge of the magnetic moment of thecompass magnet and using instrumentation located in a nonmagnetic drillcollar having a minimum length of 30 feet and in some areas of theworld, as much as 120 feet. The procedure for determination of theazimuth angle is necessarily empirical and use of the lengthynonmagnetic collar is troublesome.

In Russell et al., U.S. Pat. No. 4,163,324, there is disclosed a methodfor determination of the azimuth angle of a borehole in which it isassumed that the error vector which modifies the earth's magnetic vectorat the instrument is in the direction of the borehole at the surveylocation. The instrument can be mounted in a nonmagnetic housing in theform of a drill collar with the other components of the drill stringabove and below the instrument being typically constructed of magneticmaterials. The effect of this assumption is that the magnitude of theerror vector can be determined from the difference between the true andapparent values of the components of the earth's magnetic field in asingle direction which is not perpendicular to the axis of the borehole.

In the method of Russell et al. for determining the orientation of thesurveying instrument in the borehole, the steps include determining theinclination angle of the instrument at the location thereof in theborehole, sensing, at said location, at least one vector component ofthe local magnetic field to determine the local magnetic field in thedirection of a primary axis of the instrument aligned with the borehole,determining the azimuth angle of the instrument relative to the apparentmagnetic north direction at said location, ascertaining the truehorizontal and vertical components of the earth's magnetic field at thelocation of the borehole and determining the correction to be applied tothe apparent azimuth angle from the true and apparent values for thehorizontal and vertical components of the earth's magnetic field.

According to the invention of this Application, there is provided animproved method for determining the orientation of a surveyinginstrument in a borehole including the steps of determining theinclination angle .[.of the instrument at the location in the borehole,determining the high side angle of the instrument at the location,determining the true horizontal and vertical components of the earth'smagnetic field at the location, determining the components of the localmagnetic field perpendicular to the longitudinal axis of the instrumentat the location, determining the azimuth angle for the instrumentrelative to the apparent magnetic north direction at the location..]..Iadd.and the highside angle of the instrument in the borehole,determining two transverse components of the local magnetic fieldperpendicular to the longitudinal axis of the instrument in theborehole, determining a value for the component of the local magneticfield along the longitudinal axis of the instrument, and determining avalue of azimuth angle utilizing the local magnetic field components,the inclination angle and the highside angle. The step of determiningthe component of the local magnetic field along the longitudinal axis ofthe instrument may be accomplished by utilizing the inclination angleand data indicative of the earth's magnetic field at the borehole. Anapproximate value of the azimuth angle may also be utilized indetermining a value for the component of the local magnetic field alongthe longitudinal axis of the instrument, which may then be used todetermine a more accurate value for the azimuth angle. Such an iterationprocess may be carried out until the obtained values of azimuth angleconverge to within an acceptable error. .Iaddend.

The inclination and highside angle are preferably determined bymeasuring the gravity vector at the instrument. This may be done usingthree accelerometers which are preferably orthogonal to one another andare conveniently arranged such that two of them sense the components ofgravity in the two directions that the fluxgates sense the components ofthe local magnetic field.

.[.In another embodiment of this application, a system positioned in adrill collar is disclosed for determining the orientation of a downholeinstrument in a borehole comprising: means for determining inclinationangle of the instrument at a location in the borehole; means fordetermining the highside angle of the instrument at the location; meansfor determining the true horizontal and vertical components of theearth's magnetic field at the borehole; means for determining twocomponents of the local magnetic field perpendicular to the direction ofthe longitudinal axis of the instrument at the location, means fordetermining the azimuth angle of the instrument relative to magneticnorth direction at the location, the drill collar being constructed ofnonmagnetic material, and having a minimum length, L, which isdetermined by: ##EQU1##

.Iadd.A survey instrument according to the present invention, includingmeans for determining the inclination angle and highside angle of theinstrument and means for determining components of the local magneticfield perpendicular to the direction of the longitudinal axis of theinstrument, may be positioned within a pipe string in a borehole andutilized to determine the orientation of the instrument within theborehole by being placed within non-magnetic material in the pipe stringto allow for magnetic field measurements. The non-magnetic material maybe extended to a determinable length to separate the survey instrumentfrom magnetic material in the pipe string for the purpose of avoidingmagnetic field components transverse to the longitudinal axis of theinstrument due to magnetic interference from pipe string members..Iaddend.

The determination of the azimuth angle of an instrument in a borehole,in accordance with the invention, will now be described in more detailwith reference to the accompanying drawings in which:

FIG. 1 is a schematic elevational view of a drill string incorporating asurvey instrument in accordance with the invention.

FIG. 2 is a schematic perspective view illustrating a transformationbetween earth-fixed axes and instrument-fixed axes.

FIGS. 3 to 5 are diagrams illustrating, in two dimensions, the variousstages of the transformation shown in FIG. 2.

FIG. 6 is a block schematic diagram illustrating the instrument shown inFIG. 1.

FIG. 7 illustrates typical error in calculated azimuth as a function ofcollar length for the Gulf Coast region.

FIG. 8 is a schematic view of the survey instrument located in adrilling collar.

Referring to FIG. 1, a drill string comprises a drilling bit 10 which iscoupled by a nonmagnetic drill collar 12 and a set of drill collars 14,which may be made of magnetic material, to a drill string or pipe 16.The nonmagnetic drill collar 12 .[.of a predetermined length.]. containsa survey instrument 18 in accordance with the invention. As shown inFIG. 6, the survey instrument 18 comprises a fluxgate section 22 and anaccelerometer section 24. The accelerometer section 24 comprises threeaccelerometers arranged to sense components of gravity in three mutuallyorthogonal directions, .[.once.]. .Iadd.one .Iaddend.of which ispreferably coincident with the longitudinal axis of the drill string.The fluxgate section 22 comprises two fluxgates arranged to measuremagnetic field strength in two of the three mutually orthogonaldirections namely along axes OX and OY as will be described withreference to FIG. 2. Additionally, the survey instrument comprisesassociated signal processing apparatus as will be described hereinafterwith reference to FIG. 6.

The instrument sensors measure local field components within a"nonmagnetic" drill collar 12 which is itself part of the drill string,the collar being located close to the drilling bit 10. The outputs fromthe two mutually orthogonal fluxgates comprise the components B_(x) andB_(y) of the local magnetic field along the axes OX and OY respectively.The outputs from the three accelerometers in the accelerometer section24 comprise the components g_(x), g_(y), and g_(z) of the localgravitation field along the axes OX, OY and OZ.

The five output components g_(x),g_(y),.Iadd.g_(z), .Iaddend.B_(x) .[.,.]. and B_(y) .[.and By.]. are in the form of proportional voltageswhich are applied to a circuit processing unit 26 comprising analog todigital converters. The outputs g_(x),g_(y), and g_(z) from the analogto digital converters in the circuit processing unit 26 are ultimatelyprocessed through a digital computing unit 28 to yield values ofhighside angle φ and inclination θ. This computing operation may beperformed within the survey instrument and the computed values stored ina memory section 30 which preferably comprises one or more solid-statememory packages. However, instead of storing four values φ, θ, B_(x) andB_(y) it will usually be more convenient to provide the memory section30 with sufficient capacity to store the five outputs from the analog todigital converters in the circuit processing unit 26 and to provide thecomputing unit 28 in the form of a separate piece of apparatus to whichthe instrument is connected after extraction from the borehole.Alternatively, the values may be directly transferred to the surfaceunits via conventional telemetry means (not shown).

The instrument 18 may also comprise a pressure transducer 32 arranged todetect the cessation of pumping of drilling fluids through the drillstring, this being indicative that the survey instrument is stationary.The measurements are preferably made when the instrument is stationary.Other means of detecting the nonmovement of the instrument may be usedsuch as motion sensors.

Power for the instrument may be supplied by a battery power pack 34,downhole power generator or power line connected with a surface powersupply unit.

The preferred form of the invention, using two fluxgates and threeaccelerometers as described above, has the advantage of not requiringany accurately pivoted components, the only moving parts being the proofmasses of the accelerometers.

FIG. 2 shows a borehole 20 and illustrates various reference axesrelative to which the orientation of the borehole 20 may be defined. Aset of earth-fixed axes (ON, OE and OV) are illustrated with OV beingvertically down and ON being a horizontal reference position. Acorresponding instrument-case-fixed set of axes OX, OY and OZ areillustrated where OZ is the longitudinal axis of the borehole (andtherefore of the instrument case) and OX and OY, which are in a planeperpendicular to the borehole axis represented by a chain-dotted line,are the two above-mentioned directions in which the accelerometers andfluxgates are oriented.

A spatial survey of the path of a borehole is usually derived from aseries of measurements of an azimuth angle ψ and an inclination angle θ.Measurements of (θ, ψ) are made at successive stations along the path,and the distance between these stations is accurately known. The set ofcase-fixed orthogonal axes OX, OY and OZ are related to an earth-fixedset of axes ON, OE and OV through a set of angular rotations (ψ, θ, φ).Specifically, the earth-fixed set of axes (ON, OE, OV) rotates into thecase-filled set of axes (OX, OY, OZ) via three successive clockwiserotations; through the azimuth angle ψ about OV shown in FIG. 3; throughthe inclination angle θ, about OE shown in FIG. 4; and through thehighside angle φ, about OZ shown in FIG. 5. .[.In.]. .Iadd.If.Iaddend.U_(N), U_(E) and U_(V) are unit vectors in the ON, OE and OVdirections respectively, then the vector operation equation is:

    U.sub.NEV =[ψ][θ][φ]U.sub.XYZ                (1)

which represents the transformation between unit vectors in the twoframes of reference (ONEV) and OXYZ) where: ##EQU2## The vectoroperation equation for a transformation in the reverse direction can bewritten as,

    .[.U.sub.XYZ =(φ).sup.T (θ).sup.T (ψ).sup.T U.sub.NEV .].

    .Iadd.U.sub.XYZ =[φ].sup.T [θ].sup.T [ψ].sup.T U.sub.NEV .Iaddend.                                                 (5)

The computing operation performed by the computing unit 28 will now bedescribed. The first stage is to calculate the inclination angle θ andthe highside angle φ. Use of the vector operation equation 5 to operateon the gravity vector; ##EQU3## yields gravity components in the OXYZframe

    g.sub.x =-g sin θ cos φ                          (7)

    g.sub.y =g sin θ sin φ                           (8)

    g.sub.z =g cos θ                                     (9)

Thus, the highside angle φ can be determined from

    tan φ=-[g.sub.y /g.sub.x ]                             (10)

.Iadd.and the inclination angle from ##EQU4##.Iaddend. The next step isto obtain the value of B_(n) and B_(v), the true horizontal and verticalcomponents of the earth's magnetic field, respectively, from publishedgeomagnetic survey data .Iadd.or otherwise.Iaddend.. .[.If geomagneticsurvey data is not available, the probe itself.]. .Iadd.The probeitself, or a similar sensor with at least one fluxgate or the like,.Iaddend.may be used to measure B_(n) and B_(v) the measurement beingmade at a location close to the top of the borehole but sufficientlyremote from any ferromagnetic structure which may cause the true earth'smagnetic field to be modified. .Iadd.By "true" is meant magneticmeasurements not influenced by magnetic material of the drill string.

It will be appreciated that any data indicative of the earth's magneticfield may be determined. For example, the combination of the totalmagnetic field strength and the field dip angle is equivalent to thecombination of the north and vertical components of the field (the eastcomponent is always zero). The present calculations to obtain a correctazimuth may be effected in terms of any equivalent field data. Also,where the survey instrument or other sensor is used to determine "true"field data, the measurements need not be absolute, that is, thefluxgates need only be calibrated relative to each other. .Iaddend.

The azimuth angle, ψ, is calculated using an .[.iteration loop.]..Iadd.iterative procedure in which .Iaddend.the input values .[.being.]..Iadd.are .Iaddend.the highside angle φ, inclination angle θ, and themagnetic field components B_(x), B_(y), .Iadd.B_(v) .Iaddend.and B_(n).The initial value of azimuth angle, .[.θo.]. .Iadd.ψ_(o) .Iaddend., iscalculated from ##EQU5## Successive values of azimuth angle, .[.ψn.]..Iadd.ψ_(n) .Iaddend., may be used to determine B_(z) by equation:

    B.sub.x =B.sub.n cos ψ.sub.n sin θ+B.sub.v cos θ(12)

Using B_(z), the azimuth angle, ψ, may be determined using the equation##EQU6## Equations (12) and (13) are convenient to mechanize in acomputing step until (ψ_(n+1) -ψ_(n)) approaches a small preselectedvalue. Measurement of the local magnetic and gravitational fieldcomponents in the instrument case-fixed frame thus provides sufficientinformation to determine the azimuth value.

.Iadd.Measurements by the fluxgates must be made through non-magneticmaterial. Consequently, the drill collar 12 in the immediate vicinity ofthe fluxgate section 22 of the survey instrument 18 must be made ofnon-magnetic material. The remainder of the drill collar 12 and thedrill string in general may be constructed of magnetic material, and acorrect value for azimuth achieved with the foregoing method providedthe effect of the magnetic material on the fluxgate measurements liesonly along the longitudinal axis OZ of the survey instrument. This willbe the case provided the drill string members, such as drill collars anddrill pipe, which contribute to the measurable error in the fluxgatemeasurements, are cylindrically symmetric, for example, so that themagnetic poles of such members so interfering lie along the longitudinalaxis of the sensor instrument 18.

The source of the field of the magnetic material of a pipe string memberis distributed in an annular region which is the pipe or drill collaritself; there is no source of magnetic field along the axis of the pipeor drill collar, which is hollow. Any anisotropies in the drill stringmember, for example due to lack of concentricity between the insidediameter and the outside diameter of the member, variation in thematerial density of the member, etc., may, but won't necessarily, causethe effective magnetic pole at the end of the member to be off-axis,resulting in transverse field components along the longitudinal axis ofthe drill string at the survey instrument. At some distance from the endof a magnetic section of drill collar or drill pipe, for example manydiameters of the drill string member away, the fluxgates maynevertheless sense only a point pole along the tool axis due to themagnetic material if the transverse field due to the pipe string memberis sufficiently weak to be undetectable at such distance. However, if atransverse field is generated by the drill string member, and if thedrill string member is sufficiently close to the sensor instrument 18that the fluxgates detect the transverse field, the assumption that themagnetic flux influence due to the magnetic material in the drill stringlies only along the longitudinal axis of the survey instrument fails.

To the extent that the drill string introduces field components in atransverse direction, for example along one or both of the OX and OYaxes, measurable at the fluxgates, the value of the azimuth determinedby the foregoing method will be incorrect. However, the correct azimuthmay be determined by eliminating the transverse field components due tothe drill string from sensing by the fluxgates. This can be done byseparating the magnetic material in the drill string from the fluxgatesa sufficient distance so that the fluxgates cannot detect the transversefield effects generated by the magnetic material of the drill string.Such separation between the fluxgates and the magnetic material of thedrill string may be achieved by lengthening the section of non-magneticmaterial in which the sensor instrument 18 is located. The minimumlength of non-magnetic material, such as may be provided by the drillcollar 12, that is necessary to prevent transverse magnetic fields fromdestroying the validity of the assumption that the only field effectsdue to the drill string lie along the longitudinal axis of the sensorinstrument 18 may be calculated. The length of non- magnetic drillcollar need to avoid error due to drill string interference transverseto the longitudinal axis of the survey instrument is small compared tothat needed to avoid error in the longitudinal direction without themethod of the present invention. .Iaddend.

The length of the nonmagnetic drill collar may be determined as afunction of the tolerable transverse error field B_(err), as shown inFIG. 8 in which survey instrument 18 is located within the drill collar12 having a minimum length, L, and an outer diameter, OD. The transversefield error will be created by the proximity of the magnetic material inthe drill string 16 above and the drill collar or bit 10 below. Themagnetic material of these two sources will create poles, P_(U) andP_(L), respectively. In the worst case, the poles may be assumed to bedisplaced from center by

    d=OD/600                                                   (14)

The transverse error field may be determined by ##EQU7## where η is theangle between the axis and the poles having a vertex at the surveyinstrument 18. Therefore:

    .[.Sin η=d/(L/2)=2/d/L.]. .Iadd.sin η=d/(L/2) .Iaddend.(16)

The error caused in the azimuth angle in radians is determined byexpanding the azimuth angle in a Taylor series as a function of thetransverse field (B_(t)). ##EQU8## Therefore, the error in azimuth, δψ,is given by

    .[.δψ=(ψδ/δB.sub.t)B.sub.err .]. .Iadd.δψ=(δψ/δB.sub.t)B.sub.err .Iaddend.(18)

By definition,

    B.sub.t.sup.2 =B.sub.T.sup.2 -B.sub.z.sup.2

.Iadd.where B_(T) is the earth's magnetic field strength. .Iaddend.

Therefore:

    .[.B.sub.t (ψB.sub.t /δψ)=-B.sub.z (δB.sub.z /δψ) .]. .Iadd.B.sub.t (δB.sub.t /δψ)=-B.sub.z (δB.sub.z /δψ) .Iaddend.                  (19)

B_(t) is approximately constant between about 20,000 and 60,000 μT asdetermined from (for example) pages 75-76 of the U.S. Geological Surveypublication by E. B. Fabiano, N. W. Peddie. D. R. Barraclough and A.Zunde entitled "International Geomagnetic Reference Field 1980: Chartsand Grid Values".

From Equation (12),

    δB.sub.z /δψ=-B.sub.n sin ψsin θ (20)

Using average values, <B_(z) /B_(t) >≈1, ##EQU9## then

    δB.sub.t /δψ=B.sub.n /2                    (21)

By definition, B_(err) =(δB_(t) /δψ)δψ(21)

From equation (21)

    B.sub.err =(B.sub.n /2)δψ                        (22)

From Equation (16), ##EQU10## Solving equation (23) for L, ##EQU11## For.[.|P_(U) |+|_(L) |=2000 micro Webers.]. .Iadd.|P_(U) |+|P_(L) |=2000micro Webers .Iaddend.and a collar having an outer diameter of 71/2", d,from equation (14), equals 0.013 in. Equation (14) may vary slightlywith configuration of collar.

For an acceptable error in azimuth angle, ψ, of 0.25 degrees in the GulfCoast, the minimum nonmagnetic collar length is

L=6.4 ft.

FIG. 7 illustrates the error incurred in the calculation of azimuthangle as a function of collar length, L, for B_(n) equals 25 microTesla, a value for the Gulf Coast region. As the length of non-magneticcollar is increased, the extraneous transverse magnetic field strengthis reduced and the calculated azimuth approaches the true azimuth.

Therefore a minimum L of between about 5 to 7 feet will result in acalculated azimuth angle falling within the acceptable error region ofFIG. 7 for the Gulf Coast. Other collar lengths will be calculatedaccordingly for different regions, collar configuration and outsidediameter.

Using this determination, a system of this invention for determining theorientation of a downhole instrument in a borehole would comprise ameans for determining inclination angle of the instrument at a locationthereof in said borehole; a means for determining the highside angle ofsaid instrument at said location; .[.a means for determining the truehorizontal and vertical components of the earth's magnetic field at thelocation of the borehole;.]. a means for determining components of thelocal magnetic field perpendicular to the direction of a primary axis ofthe instrument aligned with the borehole at said location, said drillcollar being constructed of non-magnetic material, and having a minimumlength, L, determined as follows: ##EQU12##

Numerous variations and modifications may obviously be made in theapparatus herein described without departing from the present invention.Accordingly, it should be clearly understood that the forms of theinvention described herein and shown in the figures of the accompanyingdrawings are illustrative only and are not intended to limit the scopeof the invention.

What is claimed is: .[.1. A system for determining the orientation of adownhole instrument positioned in a drill collar in a boreholecomprising: a means for determining inclination angle of the instrumentat a location thereof in said borehole; a means for determining thehighside angle of said instrument at said location; a means fordetermining the true horizontal and vertical components of the earth'smagnetic field at the location of the borehole; a means for determiningcomponents of the local magnetic field perpendicular to the direction ofa primary axis of the instrument aligned with the borehole at saidlocation, said drill collar being constructed of non-magnetic material,and having a minimum length, L, determined from the equation: ##EQU13##where P_(u) is the magnetic pole created by the magnetic material abovethe sensor, P_(L) is the magnetic pole created by the magnetic materialbelow the sensor, d is the displacement of the poles P_(u) and P_(L)from the axis of the instrument, B_(n) is the North component of theearth's magnetic field at the tinstrument, and δψ is the error in theazimuth angle..]. .[.2. The orientation system of claim 1 wherein saidmeans for determining the components of local magnetic field comprises ameans for sensing measured components of said local magnetic field, saidsensing means being located at least one third of said length of saiddrill collar from an end of said drill collar..]. .[.3. The orientationsystem of claim 1 wherein said instrument is located in a drill stringextending in said borehole, said system being located between the lowerdrill string end connecting to the drill bit and an upper drill stringend connecting to the surface..]. .[.4. The orientation system of claim3 wherein said drill string is comprised of magnetic material..]..Iadd.5. A method of determining the orientation of a surveyinginstrument in a borehole comprising the steps of:a. determining theinclination angle of the instrument in the borehole; b. determininghighside angle of the instrument in the borehole; c. determining twotransverse components of the local magnetic field perpendicular to thelongitudinal axis of said instrument in the borehole; d. determining,without directly measuring, a value for the component of the localmagnetic field along the longitudinal axis of the instrument in theborehole utilizing the inclination angle; and e. determining a value ofazimuth angle of the instrument utilizing the local magnetic fieldcomponents, the inclination angle and the highside angle, and withoututilizing a directly measured value for the local magnetic fieldcomponent along the longitudinal axis of said instrument. .Iaddend..Iadd.6. A method as defined in claim 5 further comprising:a. providingdata indicative of the earth's magnetic field at said borehole; and b.using said earth's magnetic field data in the step of determining avalue for the component of the local magnetic field along thelongitudinal axis of the instrument in the borehole. .Iaddend. .Iadd.7.A method as defined in claim 6 further comprising: a. utilizing theinclination angle, the highside angle, earth's magnetic field data andsaid transverse components of the local magnetic field perpendicular tothe longitudinal axis of the instrument to obtain an approximate valueof azimuth angle; b. using the approximate value of the azimuth anglealso in determining the value for the component of the local magneticfield along the longitudinal axis of the instrument in the borehole; andc. so determining a more accurate value for azimuth angle. .Iaddend..Iadd. . A method as defined in claim 7 comprising the additional stepsof using such more accurate value of azimuth angle as an approximatevalue of azimuth angle to determine a further value for the component ofthe local magnetic field along the longitudinal axis of the instrumentin the borehole, and determining a new more accurate value of azimuthangle using said further value for the component of the local magneticfield along the longitudinal axis of the instrument as in claim 7..Iaddend. .Iadd.9. A method as defined in claim 8 comprising theadditional steps of repeating the steps of claim 8 until the obtainedvalues of azimuth angle converge to within an acceptable error..Iaddend. .Iadd.10. A method as defined in claim 6 wherein the earth'smagnetic field data is determined by utilizing sensing means included insuch a surveying instrument. .Iaddend. .Iadd.11. A method as defined inclaim 6 wherein the earth's magnetic field data is determined at thesurface of the earth in the vicinity of said borehole. .Iaddend..Iadd.12. A method as defined in claim 6 wherein the earth's magneticfield data is determined in terms of horizontal and vertical componentsof said field. .Iaddend. .Iadd.13. A method as defined in claim 5wherein said instrument is provided located in a drill string in saidborehole, said instrument being located between the lower drill stringend connecting to a drill bit and an upper drill string end connectingto the surface. .Iaddend. .Iadd.14. A method as defined in claim 5further including providing said surveying instrument positioned innon-magnetic material having a length no shorter than a length Ldetermined by the equation: ##EQU14##.Iaddend. where P_(U) is themagnetic pole of magnetic material above said non-magnetic material,P_(L) is the magnetic pole of magnetic material below said non-magneticmaterial, d is the displacement of the poles P_(U) and P_(L) from theaxis of the instrument, B_(n) is the north component of the earth'smagnetic field at the borehole, and δψ is an acceptable error in theazimuth angle. .Iadd.15. A method as defined in claim 14 wherein thetransverse components of the local magnetic field are determined byutilizing sensing means included in such a surveying instrument andlocated at least one third of said length of said non-magnetic materialfrom an end of said non-magnetic material. .Iaddend. .Iadd.16. A methodof determining the orientation of a surveying instrument in a borehole,comprising the steps of:a. determining the inclination angle of theinstrument in the borehole; b. determining the highside angle of theinstrument in the borehole; c. providing data indicative of the earth'smagnetic field at the borehole; d. determining two transverse componentsof the local magnetic field perpendicular to the longitudinal axis ofthe instrument in the borehole; e. calculating, without directlymeasuring, a value for the component of the local magnetic field alongthe longitudinal axis of the instrument in the borehole utilizing theearth's magnetic field data; and f. determining a value for the azimuthangle of the instrument utilizing said local magnetic field components,the inclination angle and the highside angle, and without utilizing adirectly measured value for the local magnetic field component along thelongitudinal axis of the instrument in the borehole. .Iaddend. .Iadd.17.A method according to claim 16 wherein said value for the component ofthe local magnetic field along the longitudinal axis of the instrumentis determined also utilizing the inclination angle and an approximationof the azimuth angle of the instrument. .Iaddend. .Iadd.18. A methodaccording to claim 17 wherein the approximation of the azimuth angle ofthe instrument is determined from the inclination angle, the highsideangle, the transverse components of the local magnetic fieldperpendicular to the longitudinal axis of the instrument, and earth'smagnetic field data. .Iaddend. .Iadd.19. A method according to claim 17comprising the additional steps of determining a further value for thecomponent of the local magnetic field along the longitudinal axis of theinstrument utilizing the previously determined value for the azimuthangle, and determining a new, more accurate value for the azimuth angleutilizing said further value for the component of the local magneticfield along the longitudinal axis of the instrument. .Iaddend. .Iadd.20.A method according to claim 19 comprising the additional steps ofrepeating the steps of claim 19 until the obtained values of azimuthangle converge to within an acceptable error. .Iaddend. .Iadd.21. Amethod according to claim 16 which comprises:a. utilizing theinclination angle, the highside angle, earth's magnetic field data andthe transverse components of the local magnetic field perpendicular tothe longitudinal axis of the instrument to obtain an approximate valueof the azimuth angle for the instrument; b. utilizing the inclinationangle and said approximate value for the azimuth angle also indetermining said value for the component of the local magnetic fieldalong the longitudinal axis of the instrument; and c. so determining amore accurate value for the azimuth angle. .Iaddend. .Iadd.22. A methodaccording to claim 21 comprising the additional steps of utilizing suchmore accurate value for the azimuth angle as an approximate value forthe azimuth angle to determine a further value for the component of thelocal magnetic field along the longitudinal axis of the instrument, anddetermining a new, more accurate value for the azimuth angle using saidfurther value for the component of the local magnetic field along thelongitudinal axis of the instrument as in claim
 21. .Iaddend. .Iadd.23.A method according to claim 22 comprising the additional steps ofrepeating the steps of claim 22 until the obtained values of azimuthangle coverage to within an acceptable error. .Iaddend. .Iadd.24. Amethod according to claim 16 wherein the local magnetic field componentsare determined by utilizing sensing means included in such a surveyinginstrument. .Iaddend. .Iadd.25. A method according to claim 16 whereinthe earth's magnetic field data is determined by utilizing sensing meansincluded in such a survey instrument. .Iaddend. .Iadd.26. A methodaccording to claim 16 wherein the earth's magnetic field data isdetermined at the surface of the earth in the vicinity of said borehole..Iaddend. .Iadd.27. A method according to claim 16 wherein saidinstrument is provided located in a drill string in said borehole, saidinstrument being located between a lower drill string end connecting toa drill bit and an upper drill string end connecting to the surface..Iaddend. .Iadd.28. Apparatus for determining the orientation of asurveying instrument in a borehole, comprising:a. means for determiningthe inclination angle for the instrument in the borehole; b. means fordetermining the highside angle of the instrument in the borehole; c.means for storing data indicative of the earth's magnetic field at theborehole; d. means for determining two transverse components of thelocal magnetic field perpendicular to the longitudinal axis of theinstrument in the borehole; e. first calculating means for calculating,without directly measuring, a value for the component of the localmagnetic field along the longitudinal axis of the instrument in theborehole utilizing the earth's magnetic field data; and f. secondcalculating means for calculating a value for the azimuth angle of theinstrument utilizing said local magnetic field components, theinclination angle and the highside angle, and without utilizing adirectly measured value for the local magnetic field component along thelongitudinal axis for the instrument in the borehole. .Iaddend.